DOI 10.1007/s10527-016-9553-y Biomedical Engineering, Vol. 49, No. 5, January, 2016, pp. 300303. Translated from Meditsinskaya Tekhnika, Vol. 49, No. 5, Sep.Oct., 2015, pp. 3537. Original article submitted July 30, 2015.
Combined Nanostructured Magnetic Field Sensor L. P. Ichkitidze*, S. V. Selishchev, D. V. Telyshev, and N. Yu. Shichkin
A combined magnetic field sensor is described. The sensor consists of a magnetically sensitive element based on giant magnetoresistance structure and a superconducting film magnetic field concentrator. Fragmentation (nanostructuring to a branch width of 20350 nm) of an active strip (narrow part) of the magnetic field concen trator in numerous branches and slits and modeling of their sizes (nanosizes) and locations allow the concentra tion coefficient and sensor efficiency to be increased by 12 orders of magnitude (resolution 10 pT). The effi ciency of the magnetic field concentrator can be further increased if lowtemperature superconductor films are used instead of hightemperature superconductor. The parameters of the suggested sensor and SQUIDs are com pared.
Introduction Various magnetic field sensors (MFSs) are used in biomedical systems. There is a particular trend towards development of magnetic systems based on spintronic MFSs. Usually, such sensors are readily available and have small mass and size and have effective functional parameters. For example, MFSs based on the effect of giant magnetoresistance (GMR) are 2 μm in width, 2 mm in length, have densities of ~1.5 g/cm3, and large flexibility (1000 cycles of deformation up to 270%) [1]. It is conceivable that an MFS of this type attached to human skin could make the person wearing the sensor sensitive to magnetic field, thus providing easier orienta tion in space. In spite of many useful characteristics of MFSs based on effects of spintronics, their sensitivity is not sufficient for many biomedical applications. For example, the reduced sensitivity of the GMR is 1 nT. In the majority of MFSs, high resolution (low δB0 < 1 nT) is achieved using super conducting magnetic field concentrators (MFC)1. In this case, MFSs mainly consist of an MFC and a magne National Research University of Electronic Technology, Zelenograd, Moscow, Russia; Email:
[email protected] * To whom correspondence should be addressed. 1 The superconducting ring performs the functions of a MFC if the detector is sensitive to magnetic field; if the detector is sensitive to magnetic flow, the superconducting ring performs the functions of a magnetic flow transformer (MFT).
tosensitive element (MSE). MSEs can be based on Josephson effect (superconducting transition), Hall sen sors, spintronic sensors, etc. [2]. Many biomedical problems can be solved using super conducting quantum interference devices (SQUIDs), which provide the highest sensitivity among MFSs (δB0 1 fT). SQUIDs use MSEs based on the Josephson effect. SQUIDs are sensitive to magnetic flow φ. Therefore, magnetic field B is measured using additional, highly expensive elements, which imposes certain limitations on the use of SQUIDs [2, 3]. Parameters comparable with those of SQUIDs were established in a new type of sensor (socalled combined MFS (CMFS)). CMFS contains a superconducting film MFC and an MSE based on spintronics (often based on GMR) [4, 5]. The literature contains descriptions of CMFS with MFCs based on lowtemperature supercon ductors (LTSC, working temperature TW ~ 4 K) and high temperature superconductors (HTSC, TW ~ 77 K). In the case of CMFS, the resolution is δB0 ~ 1 fT at TW ~ 4 K, which is significantly better than the resolution of the HTSC SQUIDs: δB0 5 fT at TW ~ 4 K. It has been demonstrated [6, 7] that optimal frag mentation (nanostructuring) of the active strip of a MFC in parallel branches and slits with nanometer size results in additional increase in the concentration coefficient and CMFS efficiency. In particular, its parameter δB becomes smaller. The combined sensor of magnetic field considered in this work consists of a magnetically sensitive element
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based on giant magnetoresistance structure and a super conducting film magnetic field concentrator. The active strip of the concentrator is fragmented into parallel superconducting branches and slits; their size (nanosize) and position are modeled.
Materials and Methods The object of the research is the multiplication factor F (concentration coefficient) of magnetic field of a film type MFC based on an MSE with nanostructuring of an active strip into superconducting branches and slits2. For a solid active strip (without fragmentation), the multipli cation factor F0 = 1. Let us consider a CMFS composed of superconducting film ring with a narrow active strip and MSE implemented as a film with GMR. An active MFC strip overlaps an MSE separated with an insulating film (Fig. 1). In an external magnetic field B0, the magnetic flow that screens a ring 1 is defined as φ = A·B0, where A is ring area. Shielding current is determined as IS = φ/(L + M), where L is ring induction; M is the sum of mutual induc tions between the MFC and the MSE. It is well known that L is an order of magnitude larger than the sum of mutual inductions M. In this case, for IS: (1) Induction L of a MFC ring is much larger than induction LS of an active strip. For the latter is composed of a few branches, each with induction Li (i = 1, 2, . . ., n + 1, where n 0 is the number of slits in the active strip), their total induction is slightly increased relative to LS. Calculations were based on wellknown equations:
(2)
(3)
2
The term multiplication factor F is used in this work as synonymous to the term multiplication factor of magnetic field g applied in [8].
Fig. 1. CMFS and its elements: 1) superconducting ring of MFC; 2) dielectric substrate; 3) active MFC strip (magnified, propor tions not maintained); 4) MSE; 5) insulating film; 6) active strip branches; 7) active strip slits.
(4)
where l and h are halfwidth and halflength, respective ly; μ0 is magnetic field constant; IS/(4hl) Jc, where IS is shielding effect of a superconducting current in active strip above the MSE and at point (x0, y0) (coordinate ori gin at the center of the top film surface); B is magnetic field in the active strip generated by the current IS; Jc and λ are density of critical current and London penetration depth for the MFC film, respectively; and are averaged values of magnetic fields generated by the active strip with or without multiple branches (solid curve), respectively; KL is growth factor of total induc tance of an active strip; L, Li are inductances of active the strip and its branch i, respectively; n is number of slits; n + 1 is number of branches in the active strip; ws, wi are full widths of the active strip and its branch i, respectively. The physical mechanism of CMFS activity is based on concentration of magnetic field using a MFC with a MSE. High concentration of magnetic field in the MSE allows its magnetic sensitivity S0 to be increased by F0 and CMFS resolution to be improved. Here S0 = (RB – R0)/(R0 · B0), where RB is MSE resistance in an external magnetic field, i. e. R0 ≠ 0; R0 is MSE resistance in the absence of external magnetic field, i. e. B0 = 0. F0 increas es the S0 as ~ F0·S0. Therefore, useful characteristics of the MFS are improved (minimal detectable magnetic field δB0 becomes smaller). A CMFS with solid active strip is characterized by the following relationship:
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(5) where δU is minimal detectable signal of the MSE; I is measuring current of the MSE. It can be seen that high F value improves parameters of the MFS, i.e. decreases δB0. Taking into account Eq. (1), F0 is found to be (according to the definition): (6)
(7)
(8)
(9) where induction L of the ring, its diameter D, width wL, as well as magnetic field Ba at the active strip surface gener ated by current IS, are taken into account.
Results and Discussion
B, T
In all calculations, the following numerical parame ters of the suggested CMFS were used: D = 4 mm – ring
x, μm Fig. 2. Nonuniform distribution of magnetic field over an active strip of a magnetic field concentrator and its mean value in super conducting films of different materials. LTSC: λ = 50 nm; 1 – B; 2 – ; HTSC: λ = 250 nm; 3 – B; 4 – .
diameter; wL = 1.7 mm – contour width; ws = 7 μm – active strip width; h = 25 nm – active strip halfwidth; λ = 50 nm – London penetration depth for LTSC mate rial; λ = 250 nm – London penetration depth for HTSC material; μ0 = 1.256·10–6 H/m – magnetic field constant. Let us consider several cases. 1. Let external magnetic field be B = 10 μT, Jc > 1011 A/m2. Homogeneous distribution of current in the active strip is considered. In this case, F0 ~ 259 in accor dance with the given equations, i.e. the concentration coefficient is rather high. In other words, the magnetic field in the active strip is 259 times larger than outside the strip. 2. For superconducting films used as a magnetic field concentrator, the distribution of the current is nonuni form (especially across the width of the active strip). Therefore, F0 becomes smaller. A typical pattern of distribution of magnetic field over the active strip at different values of λ is shown in Fig. 2. Figure 2 shows that external magnetic field is con centrated in an active strip. For example, the peak field (~34 mT) is several thousand times greater than the exter nal magnetic field (~10 μT). However, its mean value averaged over active strip width is much smaller. The fol lowing values of the multiplication factor were obtained: at λ = 50 nm – 174; at λ = 250 nm – 216 (mean value of was calculated from Eq. (2)). It can be seen that F0 is less than the ideal value 259 (case 1) obtained when the current distribution over the active strip is uniform. 3. If i = 1 and n = 0, F = 1, which corresponds to a MFC with solid active strip. F value changes considerably in case of fragmentation (i > 1) of the active strip into par allel branches and slits (Fig. 1). In the simple case of two slits (n = 2), the multiplication factor increases 24 times depending on their position in the active strip. Small F is observed if slits are near edges, while maximal values of F are observed if slits are far from active strip edges. The F(n) dependences for different values of λ are shown in Fig. 3. The same parameters as above are used for calculations. The thickness of the insulation layer hins = 20 nm and Jc > 1011 A/m2 are used as additional parameters. An increase in the number of nanoslits in the active strip surface leads to a considerable increase in the con centration factor F. However, as the number of slits reaches a certain limit, the effect is inverted. It is shown in Fig. 3a that at λ = 50 nm and ws = 20 nm, F is maxi mal, but if the number of slits is 64, the monotonic increase ceases and a decrease begins. The observed max imum is Fm = 45. Similarly, at λ = 250 nm and ws = 20 nm, Fm is maximal (Fm = 11) at n = 32 (Fig. 3b). Comparative analysis of the concentration factors at λ = 50 nm and λ = 250 nm demonstrated that in the first case F value was four times larger than in the second case.
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b
Fig. 3. Dependence F(n): a) λ = 50 nm; b) λ = 250 nm for different ws (nm): 1) 20; 2) 40; 3) 60; 4) 80; 5) 100; 6) 350.
High value of F ~ 44 at low values of λ demonstrated greater efficiency of pure LTSC materials (e.g. heteroepi taxial layers (HEL) of niobium λ ~ 60 nm [9]) as compared to granular or HTSC materials, where Fm ~ 11 (e.g. ceram ics Bi2223 with λ ~ 250 nm [10]) used in film MFC. The goal of this work was to discuss the case of active strip fragmentation into superconducting branches and slits (nonsuperconducting branches) of nanometer size. In this work (D = 4 mm, wL = 7 μm; other parameters the same as used before), F0 ~ 200, Fm ~ 50, total multiplica tion factor (concentration coefficient) F0·Fm > 10000 and δB < 10–14 T according to Eq. (5). Thus, to decrease δB it was not necessary to increase D or to decrease ws, as fol lows from Eq. (7).
Conclusion Medical magnetic systems (e.g. magnetocardio graph, magnetoencephalograph (MEG), and lowfield magnetic resonance tomographs) are the main types of systems using MFS with magnetic field resolution < 10 pT. Such systems are equipped with SQUIDs based on superconducting film MFC (MFT) with size D ~ 7 10 mm. Large size of SQUIDs imposes a limit on their use in large numbers (several hundreds) for improving the useful characteristics of these magnetic systems. On the other hand, the CMFS described in this work allows the size D to be reduced severalfold (e.g. D < 1 mm), while the parameters of a CMFS with solid active strip (D > 4 mm) are kept intact. It is beyond doubt that the CMFS suggested in this work has significantly small er size and mass than SQUIDs of comparable resolution. This increases the number of possible MFS in magnetic systems. For example, in the MEG helmet available from Elekta there are 306 SQUIDs [11]. However, they can be
replaced by 1000 CMFSs, which widens the functional range of magnetoencephalography. Presently, new methods of diagnosis and therapy are widely introduced into medical practice together with new biocompatible materials (nanomaterials with ferromagnet ic and supermagnetic particles, carbon nanotubes, etc.). Noninvasive diagnosis and monitoring of operation of active implanted apparatuses (artificial heart, various stim ulators, blood flow monitors, etc.) are also urgent prob lems. We believe that important medical problems can be solved using combined sensors of magnetic field based on nanostructured active strips suggested in this work. We are grateful to Prof. V. M. Podgaetsky for stimu lating discussion. This work was supported by the Russian Science Foundation (Project No. 143900044). REFERENCES 1. Melzer M., Raltenbrunner M., Makarov D., et al., Nature Commun., 6, 6080 (2015). 2. Robbes D., Sensors Actuators A: Physical, 129, No. 1, 8693 (2006). 3. Drung D., Assmann C., Deyer J., et al., IEEE Trans. Appl. Supercond., 17, 699704 (2007). 4. PannetierLecoeur M., et al., Science, 304, No. 5677, 16481650 (2004). 5. PannetierLecoeur M., Superconductingmagnetoresistive Sensor: Reaching the femtotesla at 77 K: Dissertation, Universitй Pierre et Marie Curie, Paris VI (2010), pp. 3234. 6. Ichkitidze L., Mironyuk A., Physica C: Superconductivity, 472, No. 1, 5759 (2012). 7. Ichkitidze L. P., Mironyuk A. N., “A Superconductor Film Transformer of Magnetic Flux”, RF Patent No. 2455732. 8. PannetierLecoeur M., et al., Appl. Phys. Lett., 98, No. 15 (2011). 9. Ichkitidze L. P., Skobelkin V. I., Bablidze R. A., Fiz. Tverd. Tela, 27, No. 10, 31163119 (1985). 10. Ichkitidze L. P., Bull. Russ. Acad. Sci. Phys., 71, No. 8, 11451147 (2007). 11. www.mrn.org/collaborate/elektaneuromagmeg
